OFFSET
0,1
COMMENTS
a(0) has been checked by the direct computation of the Wiener index (using Maple).
LINKS
H. Yousefi-Azari, A. R. Ashrafi, and M. H. Khalifeh, Wiener index of micelle-like chiral dendrimers, Studia UBB, Chemia, 55, No. 4, 125-130, 2010.
Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).
FORMULA
a(n) = 2979 + 13680*2^n + 131200*4^n + 52224*n*4^n + 30240*n*2^n + 36864*n^2*4^n + 6336*n^2*2^n.
a(n) = 19*a(n-1)-150*a(n-2)+636*a(n-3)-1560*a(n-4)+2208*a(n-5)-1664*a(n-6)+512*a(n-7). [Bruno Berselli, Apr 06 2013]
G.f.: -(13735424*x^6 -40286592*x^5 +47779680*x^4 -29472552*x^3 +10001292*x^2 -1824678*x +147859) / ((x-1)*(2*x-1)^3*(4*x-1)^3). [Colin Barker, Apr 15 2013]
MAPLE
a := proc (n) options operator, arrow: 2979 + 36864*4^n*n^2 + 13680*2^n + 30240*2^n*n + 52224*4^n*n + 6336*2^n*n^2 + 131200*4^n end proc: seq(a(n), n = 0 .. 15);
MATHEMATICA
a = {147859, 984643, 6530659, 40951843, 241838755, 1355802019, 7283759011}; Do[AppendTo[a, 19 a[[-1]] - 150 a[[-2]] + 636 a[[-3]] - 1560 a[[-4]] + 2208 a[[-5]] - 1664 a[[-6]] + 512 a[[-7]]], {10}]; a (* Bruno Berselli, Apr 06 2013 *)
PROG
(Magma) [2979+13680*2^n+131200*4^n+52224*n*4^n+30240*n*2^n+ 36864*n^2*4^n+6336*n^2*2^n: n in [0..25]]; // Vincenzo Librandi, Nov 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 06 2013
STATUS
approved